Nathan Bloomfield wrote:
> Hello haskell-cafe;
>> I'm fiddling with this
> <http://cdsmith.wordpress.com/2009/07/20/calculating-multiplicative-inverses-in-modular-arithmetic/>
> blog post about inverting elements of Z/(p), trying to write the
> inversion function in pointfree style. This led me to try executing
> statements like
>> n `mod` 0
>> which in the ring theoretic sense should be n, at least for integers*.
> (MathWorld agrees. <http://mathworld.wolfram.com/Congruence.html>)
I agree that (n `mod` 0) ought to be n. Specifically
divMod n 0 = (0,n)
and
quotRem n 0 = (0,n)
In (divMod n m) the sign of the remainder is always the same as the sign
of m, unless n or m is zero. In (quotRem n m) the sign of the quotient
is the product of the signs of n and m, unless n or m is zero.
--
Chris